{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# p22: 5'th eigenvector of Airy equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='svg'\n",
    "from chebPy import *\n",
    "from numpy import dot,diag,real,argsort,zeros,linspace,polyval,polyfit,where\n",
    "from scipy.linalg import eig\n",
    "from scipy.special import airy\n",
    "from matplotlib.pyplot import figure,subplot,plot,title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/praveen/Applications/anaconda/lib/python2.7/site-packages/numpy/lib/polynomial.py:595: RankWarning: Polyfit may be poorly conditioned\n",
      "  warnings.warn(msg, RankWarning)\n"
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   "source": [
    "figure(figsize=(10,8))\n",
    "for N in range(12,60,12):\n",
    "    D,x = cheb(N); D2 = dot(D,D); D2 = D2[1:N,1:N]\n",
    "    Lam,V = eig(D2,diag(x[1:N]))\n",
    "    Lam = real(Lam); ii = where(Lam>0)[0]\n",
    "    V = real(V[:,ii]); Lam = Lam[ii]\n",
    "    ii = argsort(Lam); ii=ii[4]; Lam=Lam[ii]\n",
    "    v = zeros(N+1); v[1:N] = V[:,ii]; v = v/v[N/2]*airy(0.0)[0]\n",
    "    xx = linspace(-1.0,1.0,200); vv = polyval(polyfit(x,v,N),xx);\n",
    "    subplot(2,2,N/12); plot(xx,vv)\n",
    "    title(\"N = %d   eig = %15.10f\"%(N,Lam));"
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